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References

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  1. O. Kafri, “Noncoherent Method for Mapping Phase Objects,” Opt. Lett. 5, 555 (1980).
    [CrossRef] [PubMed]
  2. E. Keren, E. Bar-Ziv, I. Glatt, O. Kafri, “Measurements of Temperature Distribution of Flames by Moire Deflectometry,” Appl. Opt. 20, 4263 (1981).
    [CrossRef] [PubMed]
  3. L. Horowitz, Y. B. Band, O. Kafri, D. F. Heller, “Thermal Lensing Analysis of Alexandrite Laser Rods by Moire Deflectometry,” Appl. Opt. 23, 2229 (1984).
    [CrossRef] [PubMed]
  4. E. Keren, A. Livnat, I. Glatt, “Moire Deflectometry with Pure Sinusoidal Gratings,” Opt. Lett. 10, 167 (1985).
    [CrossRef] [PubMed]
  5. M. Cetica, F. Francini, D. Bertani, “Moire with One Grating and Photodiode Array,” Appl. Opt. 24, 1565 (1985).
    [CrossRef] [PubMed]
  6. E. Bar-Ziv, “Effect of Diffraction on the Moire Image. I: Theory,” J. Opt. Soc. Am. A 2, 371 (1985).
    [CrossRef]
  7. E. Bar-Ziv, S. Sgulim, D. Manor, “Effect of Diffraction on the Moire Image. II: Experiment,” J. Opt. Soc. Am. A 2, 380 (1985).
    [CrossRef]
  8. G. Eichmann, Y. Li, R. R. Alfano, “Digital Optical Logic Using a Pulsed Sagnac Interferometer Switch,” Opt. Eng.25, in press (1986).
    [CrossRef]

1985 (4)

1984 (1)

1981 (1)

1980 (1)

Alfano, R. R.

G. Eichmann, Y. Li, R. R. Alfano, “Digital Optical Logic Using a Pulsed Sagnac Interferometer Switch,” Opt. Eng.25, in press (1986).
[CrossRef]

Band, Y. B.

Bar-Ziv, E.

Bertani, D.

Cetica, M.

Eichmann, G.

G. Eichmann, Y. Li, R. R. Alfano, “Digital Optical Logic Using a Pulsed Sagnac Interferometer Switch,” Opt. Eng.25, in press (1986).
[CrossRef]

Francini, F.

Glatt, I.

Heller, D. F.

Horowitz, L.

Kafri, O.

Keren, E.

Li, Y.

G. Eichmann, Y. Li, R. R. Alfano, “Digital Optical Logic Using a Pulsed Sagnac Interferometer Switch,” Opt. Eng.25, in press (1986).
[CrossRef]

Livnat, A.

Manor, D.

Sgulim, S.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of a single-grating moire system for the mapping of ray deflections from phase objects: O, phase object; G, grating; P, right-angle prism; MS, matte screen; D, prism parameter; l, adjustable distance.

Fig. 2
Fig. 2

Geometrical relationships between the maximum input object size S and parameters Φmax, d, and D: (a) geometry for the basic single-grating setup (see Fig. 1); (b) geometry for the modified setups (see Fig. 3).

Fig. 3
Fig. 3

Two modified single-grating moire systems: O and I, phase object and its image; L1 and L2, two Fourier transform lenses, G, grating; P, right-angle prism; BS, beam splitter; MS, matte screen. (a) For identical focal length lenses, the direct deflections from the object are mapped. (b) For focal length of the lens L1 larger than L2, the deflections from the image of the object are mapped.

Fig. 4
Fig. 4

Experimental reference moire patterns using the setup of Fig. 3(b). The grating pitch period is 0.5 mm, and the focal length ratio is four. The grating is rotated θ/2 in (a) about the y direction and in (b) about the x direction. (c) The result of a filtered image of Fig. 4(b).

Equations (9)

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p = p 2 sin ( θ / 2 ) .
Φ ( x ; y ) = 2 h ( x ; y ) tan ( θ / 2 ) 2 l + 2 D / n ,
Δ = 2 l + 2 n D ,
D < p 2 2 n λ ,
S < D ( 1 8 d Φ max 2 n ) 2 d Φ max .
S < 2 D ( 1 4 d Φ max 2 n ) 2 d Φ max .
p = p 2 sin ( θ / 2 ) ( f 1 f 2 ) .
Φ ( x ; y ) = 2 h ( x ; y ) tan ( θ / 2 ) 2 l + 2 D / n ( f 2 f 1 ) 2 ,
q = R R = f 1 f 2 .

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